Kelly S. Cromer was fourth, with 1,862 votes. Parson received 1,837 votes.
The highest Republican finisher was Scott D. Hesse, who had 1,792 votes, for sixth place.
Hesse was one of five Republican council candidates running as a slate along with Trump.
The Washington County Board of Elections had received 196 absentee ballots as of Tuesday, the deadline for them to be returned, Election Director Dorothy Kaetzel said.
Up to 14 more absentee ballots could be counted if the board receives them today and the ballots were postmarked before today, Kaetzel said.
Absentee ballots are scheduled to be counted Thursday.
The number of absentee ballots gives Hesse, and possibly other Republicans, a theoretical chance at moving up and taking at least one council seat.
Hesse did not return a call for comment late Tuesday.
Of the city's 18,906 registered voters - a majority of whom are Democrats - 4,245 voted Tuesday, which is 22.5 percent.
The 2001 general election turnout was 17.3 percent.
Aleshire was the only council candidate to hear the results firsthand at the Board of Elections office.
He immediately pulled out a cell phone and called a close friend to share the news.
Aleshire said money matters made a difference in the race.
"This city is not for sale, no matter how much money," he said, referring to the Republicans' substantially higher campaign fundraising and spending. "Money is a very, very poor substitute for intelligence."
Aleshire then went to Parson's campaign headquarters on North Potomac Street, where the mood was joyous after the cumulative results were announced.
Parson - who advanced in the March Democratic primary by one vote - wouldn't allow herself to celebrate too much Tuesday, considering how close the race was.
But she celebrated the people who worked and campaigned for her, pointing each one out by name, and she hugged Aleshire.
Parson said her campaign message was "inclusiveness."
Parson's husband, Godfrey McBean, didn't mind looking ahead to her possible role in city government, even with a Republican mayor.
"My wife is a good listener and she works good with people, whether Democratic, Republican or Independent," he said.
In the city's history, there have been few black candidates for City Council and no winners. The last black candidate is believed to have been Robert H. Kelsh in 1973.
Aleshire said he isn't worried about serving with a Republican mayor, stressing the council's strength over the mayor, who doesn't vote.
The party of the mayor matters far less than the mayor's policies, Metzner said.
Voters apparently rejected the Republican slate's criticism of the current administration over Washington County Hospital's proposed move to Robinwood Drive, Metzner said.
"I think people saw my sincerity and that I had integrity ... and that I was believable ...," Cromer said. "I don't think that came from the slate. The slate was all about raising $65,000."
Council members serve four years and are paid $8,000 a year. They also are eligible for health benefits through the city.
The new administration takes office May 30.